Quill: 3D QED particle-in-cell code
Quill (simulator for QUantum effects in Intense Laser–pLasma interactions) is an open-source fully three-dimensional parallel particle-in-cell code developed in the Institute of Applied Physics RAS. To our knowledge, it is the first particle-in-cell code with implementation of Monte Carlo QED approach to investigate electron–positron cascades development in electromagnetic field.
The source code is available at github.com.
The code is able so model the following processes using Monte Carlo technique:
- photon emission by an electron in the strong field, with radiation reaction effects;
- electron–positron pair creation from gamma photons (Breit–Wheeler process);
- electron–positron pair birth from vacuum in extremely strong fields;
- field ionization.
The Maxwell solvers implemented in the code are FDTD, NDFX (the scheme used in A. Pukhov's VLPL code DOI: 10.1017/S0022377899007515), and hybrid five-point FDTD (the scheme reduces numerical Cherenkov instability DOI: 10.1088/1742-6596/1692/1/012002).
The particle pushers implemented in the code use the Boris, Vay, and Higuera–Cary schemes.

Papers that contain results obtained with Quill:
E.N. Nerush, I.Yu. Kostyukov, et al. Laser Field Absorption in Self-Generated Electron-Positron Pair Plasma // Phys. Rev. Lett. 106, 035001 (2011).
E.N. Nerush, I.Yu. Kostyukov. Modelling of QED effects in superstrong laser field // Voprosy Atomnoj Nauki i Tekhniki 68 (4), 3–7 (2010).
E.N. Nerush, I.Yu. Kostyukov. Carrier-envelope phase effects in plasma-based electron acceleration with few-cycle laser pulses // Phys. Rev. Lett. 103, 035001 (2009).
N.V. Elkina, A.M. Fedotov, I.Yu. Kostyukov, et al. QED cascades induced by circularly polarized laser fields // Phys. Rev. STAB. 14, 054401 (2011).
A. Samsonov, A. Pukhov, and I. Kostyukov. Superluminal phase velocity approach for suppression of Numerical Cherenkov Instability in Maxwell solver // J. Phys.: Conf. Ser. 1692, 012002 (2020).
A.A. Soloviev, M.V. Starodubtsev, et al. Two-screen single-shot electron spectrometer for laser wakefield accelerated electron beams // Rev. Sci. Instrum. 82, 043304 (2011).
V.F. Bashmakov, E.N. Nerush, I.Yu. Kostyukov, et al. Effect of laser polarization on quantum electrodynamical cascading // Phys. Plasmas 21, 013105 (2014).
E.N. Nerush, I.Yu. Kostyukov, et al. Gamma-ray generation in ultrahigh-intensity laser-foil interactions // Phys. Plasmas 21, 013109 (2014).
E.N. Nerush, I.Yu. Kostyukov. Laser-driven hole boring and gamma-ray emission in high-density plasmas // Plasma Phys. Control. Fusion 57(3), 035007 (2015).
D.A. Serebryakov, E.N. Nerush, and I.Yu. Kostyukov. Incoherent synchrotron emission of laser-driven plasma edge // Phys. Plasmas 22, 123119 (2015).
A.A. Golovanov, I.Yu. Kostyukov, et al. Beam loading in the bubble regime in plasmas with hollow channels // Phys. Plasmas 23, 093114 (2016).
D.A. Serebryakov, E.N. Nerush. Efficient gamma-ray generation by ultra-intense laser pulses obliquely incident on a planar plasma layer // Quantum Electronics 46(4), 299–304 (2016).
I.I. Artemenko, I.Yu. Kostyukov. Ionization-induced laser-driven QED cascade in noble gases // Phys. Rev. A 96, 032106 (2017).
A.S. Samsonov, E.N. Nerush, and I.Yu. Kostyukov. Laser-driven vacuum breakdown waves // Scientific Reports 9(1), 1–11 (2019).
D.A. Serebryakov, T.M. Volkova, E.N. Nerush, and I.Yu. Kostyukov. Efficient gamma-ray source from solid-state microstructures irradiated by relativistic laser pulses // Plasma Phys. Control. Fusion 61(7), 074007 (2019).
A.S. Samsonov, I.Yu. Kostyukov, and E.N. Nerush. Hydrodynamical model of QED cascade expansion in an extremely strong laser pulse // Matter and Radiation at Extremes 6(3), 034401 (2021).
A.S. Samsonov, E.N. Nerush, and I.Yu. Kostyukov. Beamstrahlung-enhanced disruption in beam-beam interaction // New Journal of Physics 23, 103040 (2021).